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Math Help - Find the solution set?

  1. #1
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    Find the solution set?

    Use the given root to find the solution set of the polynomial.
    Polynomial: x^4 - 4x^3 + 2x^2 - 4x + 1 = 0
    Given root: i

    How do I solve this problem?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by tsmith View Post
    Use the given root to find the solution set of the polynomial.
    Polynomial: x^4 - 4x^3 + 2x^2 - 4x + 1 = 0
    Given root: i

    How do I solve this problem?
    Hi tsmith,

    If one of the roots is i, then one of the roots is also -i.

    (x - i) and (x + i) are factors.

    Their product is x^2+1

    Use polynomial long division on your original function to find the depressed quadratic.

    I think you'll discover it's x^2-4x+1

    Now, use the quadratic formula to discover the last two roots.
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